A.  \(33\frac{2}{6}\)
B.  \(36\frac{8}{3}\)
C.  \(34\frac{4}{2}\)
D.  \(31\frac{5}{7}\)

Answer:

D.  \(31\frac{5}{7}\)

Solution:

\[\left. \begin{array}{l}\\ { \text {Sum of the Ages of Grand Parents:}}\\ { \text {Avg Age=}}\frac{\text {Sum of Ages}}{\text {Total Persons}}\\ 67=\frac{\text {Sum of Ages}}{2}\\ \text {Sum of Ages}=67\times2=134 …(a)\\ { \text {Sum of the Ages of Parents:}}\\ =35\times2=70 … (b)\\ { \text {Sum of the Ages of Children:}}\\ =6\times3=18 ….(c)\\ { \text {Total Family Members:}}\\ =2+2+3=7 ….(d)\\ { \text {Average Age of family=}} (\frac{\text {Sum of the Ages}}{\text {Total Persons}}) \\ { \text {Average Age of family=}} (\frac{a+b+c}{d}) \\ { = ( \frac { 134 + 70 + 18 } { 7 } ) }\\{ = \frac { 222 } { 7 } }\\{ = 31 \frac { 5 } { 7 } \text { years. } }\end{array} \right.\]

A. Rs. 5081
B. RS. 4810
C. RS. 4991
D. Rs. 4972

Solution:

\begin{array} { l } \bf \text { Data we Have: }\\ \text { Required Avg Sale for 6 month= 6500 }\\ \text { Total Number of months= 6 }\\ { \text { Total sale for } 5 \text { months =}} \\ \Rightarrow{ R s . ( 6435 + 6927 + 6855 + 7230 + 6562 )}\\ { \Rightarrow \text { Rs. } 34009 \text { } } \\ \text { Formula for the required sale will be:}\\ \text { Required Sale = }\frac{\text { Sum of Sale of 6 months }}{\text { Total number of Months }}\\ \\ \bf \text { By Putting the values we get:}\\ 6500= \frac{\text { Sum of Sale of 6 months }}{6}\\ \text { Sum of Sale of 6 months= }6500\times6=39000\\ { \therefore \text { Required sale } = ( 39000 -\text { 5 month sale )} } \\ { = R s . ( 39000 – 34009 ) } \\ { = \text { Rs. } 4991 } \end{array}

A. 84 kg
B. 81 kg
C. 80 kg
D. 85 kg

Solution:

 

\[\left. \begin{array} { l }\text {Average weight of each person = 65kg} \\ \text {Avg weight of each person increased = }2.5kg\\ \text {Total avg weight of 8 persons increased by:} \\ 8\times2.5=20kg\\ \text {Since total weight increased is actually} \\ \text {the weight of new person. Therefore,}\\ \text { The weight of new person = 65+20= 85KG}\\ \end{array} \right.\]

A. 20 years
B. 27 years
C. 21 years
D. 23 years

Solution:

\[\left. \begin{array} { l } \text {Captain Age = 26 years}\\ \text {Wicket Keepers age = 26+3= 29 years}\\ \text {Let the average age of team be x years}\\ \text {So, avg age of 9 players would be = 9(x-1)}\\ \text {Total number of players = 11}\\ \text {Putting the values in the formula we get:}\\ \text {Avg age of team =}\frac{\text {Sum of the Ages of Players}}{\text {Total number of Players}}\\ \text {x = } \frac{26+29+9(x-1)}{11}\\ \text {11 = 55 + 9x – 9}\\ \text {11x – 9x = 46}\\ \text {2x = 46} \text {x = 23 years} \end{array} \right.\]

\[\left. \begin{array} { l }\text {Avg monthly income of P and Q =5050 }\\ \text {Sum of incomes of P and Q is:}\\ \text {Avg income =} \frac{\text {Sum of Incomes}}{\text {Total Number of persons}}\\ \Rightarrow \text {5050 =} \frac{P+Q}{2}\\ \text {P+Q = 5050}\times 2\text {= 10100 …(i)}\\ \text {Likewise:} \text {Q+R = 6250}\times 2\text {= 12500 …(ii)}\\ \text {P+R = 5200}\times 2\text {= 10400 …(iii)}\\ { \text { Now adding (i), (ii) and (iii), we get: }}\\ \Rightarrow { 2 ( P + Q + R ) = 33000}\\ \text { P + Q + R= 16500 …(iv) } \\ { \text { Subtracting (ii) from (iv), we get } P = 4000 } \\ { \therefore \text { P’s monthly income } = \text { Rs. } 4000 } \end{array} \right.\]

A. 8.71
B. 7.98
C. 6.87
D. 9.99

 

\[\left. \begin{array} { l } \text {Total expenditure on petrol each year = 4000}\\ \text {Petrol consumption in 1st year = }\frac{4000}{7.5}\\ \text {Petrol consumption in 2nd year = }\frac{4000}{8}\\ \text {Petrol consumption in 3rd year = }\frac{4000}{8.50}\\ \text {Total quantity of petrol consumed in 3 years:}\\ \Rightarrow ( \frac { 4000 } { 7.50 } + \frac { 4000 } { 8 } + \frac { 4000 } { 8.50 } ) \text { litres } \\ { = 4000 ( \frac { 2 } { 15 } + \frac { 1 } { 8 } + \frac { 2 } { 17 } ) \text { litres } }\\ {= ( \frac { 76700 } { 51 } ) \text { litres } }\\ { \text { Total amount spent } = \text { RS. } ( 3 \times 4000 )}\\ {= \text { Rs. } 12000 \text { . } } \\ { \therefore \text { Average cost } = \text { Rs. } ( \frac { 12000 \times 51 } { 76700 } ) }\\ {\text {= Rs. } \frac { 6120 } { 767 } = Rs 7 .98 } \end{array} \right.\]